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24 lines
625 B
Markdown
24 lines
625 B
Markdown
---
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cards-deck: default_obsidian
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---
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## monotone
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$a_{n}<a_{n}+1$ increasing
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$a_{n}>a_{n}+1$ decreasing
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Can be used to define limits.
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## Bounds
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### bounded above
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There is a $M$ such that $a_{n}\le M$ for all $n>1$
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### bounded below
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There is a $m$ such that $a_{n}\ge m$ for all $n>1$
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## monotone and bounded convergent
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Definition of 'bounded' ::: Bounded from both above and below. ^1653317426701
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You have to specify if it's just above or just below.
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The [[sequences|sequence]] is [[convergence and divergence of series.|convergent]] if it's monotone + bounded in its direction, or if it's generally monotone+bounded.
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